Speciation rates vary considerably among lineages, and our understanding of what drives the rapid succession of speciation events within young adaptive radiations remains incomplete1–11. The cichlid fish family provides a notable example of such variation, with many slowly speciating lineages as well as several exceptionally large and rapid radiations12. Here, by reconstructing a large phylogeny of all currently described cichlid species, we show that explosive speciation is solely concentrated in species flocks of several large young lakes. Increases in the speciation rate are associated with the absence of top predators; however, this does not sufficiently explain explosive speciation. Across lake radiations, we observe a positive relationship between the speciation rate and enrichment of large insertion or deletion polymorphisms. Assembly of 100 cichlid genomes within the most rapidly speciating cichlid radiation, which is found in Lake Victoria, reveals exceptional ‘genomic potential’—hundreds of ancient haplotypes bear insertion or deletion polymorphisms, many of which are associated with specific ecologies and shared with ecologically similar species from other older radiations elsewhere in Africa. Network analysis reveals fundamentally non-treelike evolution through recombining old haplotypes, and the origins of ecological guilds are concentrated early in the radiation. Our results suggest that the combination of ecological opportunity, sexual selection and exceptional genomic potential is the key to understanding explosive adaptive radiation.